The in-form American had looked due for a victory this year and finished the PGA Tour event at 11 under, a shot clear of Englishman Luke Donald.
Kuchar, who had six top-10 finishes this season heading into the tournament, holed out of a bunker on the 18th to set up his win.
He had earlier gone on a stunning run on the front nine – producing six birdies – and another at the 10th left him at seven under for the day at Harbour Town Golf Links.
Kuchar nervously three-putted the par-three 17th from four feet, but made up for that mistake with a stunning chip out of the bunker on 18 to go into a one-shot lead.
Overnight leader Donald was unable to match that as he holed six consecutive pars to finish the tournament.
The win was Kuchar's seventh on the PGA Tour and first since he claimed The Memorial Tournament in June 2013.
Donald, who held a two-shot overnight lead in South Carolina, was left to rue a double bogey at the par-four sixth.
American duo Ben Martin (67) and John Huh (68) were tied for third at nine under, two shots clear of countrymen Scott Brown (67) and Brian Stuard (68).
Jim Furyk (70) and Brian Harman (69) were a further shot back at six under and tied for seventh.
South African Rory Sabbatini (68), Scot Russell Knox (70) and American William McGirt (66) finished at five under.
Fresh from his runner-up finish at the Masters, 20-year-old American Jordan Spieth enjoyed another strong showing as he tied for 12th.
Northern Irish defending champion Graeme McDowell (70) was consistent throughout as he ended up tied for 23rd.